Different types of mathematical model for proton exchange membrane fuel cells and fuel cell stacks have been analysed. Developing models can help us to understand the transfer and reaction phenomena occurring in fuel cells and fuel cell stacks, predict fuel cells performance and optimize operating and structure parameters of fuel cell system. The model types are as follows: (1) Computational fluid dynamics models for single fuel cell; (2) Models described the relationship between voltages and current densities for both single cell and stacks; (3) Models described gas distribution in fuel cell stacks; (4) Models described fuel cell systems; and (5) Transient models.